"...it will of course still be infinite, but the distances between all points on the manifold will increase..."
Just a thought here, Neutralino, but have you thought through the above implications?
If you're referring to a universe whereby the potential expansion into "nothingness" is eternal, then eternity and infinity can be equated; but if by infinite you imply that all points are expandable, then in which direction would the universe expand? Any and all points would be expanding in all directions, and therefore contracting as well because they would be expanding into each other.
Could you explain your argument more thoroughly if you have the time? Lloyd had tried to explain a similar position, but I just can't figure out how it can be possible outside of a finite framework.
Here's a simple analogy to maybe assist the thinking behind an infinite universe expanding (well, the distances between all points in an infinite universe increasing). Suppose I have a number line; let's take the natural numbers (the integers 1,2,3,....) for simplicity. Now, if I double each number then this has the effect of increasing the distance between one point and every other; that is we now have the set of even positive integers; 2,4,6,... Note that both sets are infinite (in fact they are precisely the same size) but the distances between the points in the second set are larger than those in the first set.
~neutralino
If you haven't found something strange during the day, it hasn't been much of a day - John A. Wheeler.
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"...it will of course still be infinite, but the distances between all points on the manifold will increase..."
Just a thought here, Neutralino, but have you thought through the above implications?
If you're referring to a universe whereby the potential expansion into "nothingness" is eternal,
Note that I never said that the universe "expands into" anything. The definition of "universe" is everything that exists; whether that be spacetime, or matter inside that spacetime. The universe may be infinite, or it may be finite; we don't really know yet. We do know, however, that the observable universe is much smaller than the total universe such that we can think of the universe as being infinite.
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then eternity and infinity can be equated; but if by infinite you imply that all points are expandable, then in which direction would the universe expand? Any and all points would be expanding in all directions, and therefore contracting as well because they would be expanding into each other.
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You're talking about "expansion of points" here, whereas I'm not. Points have no size, and so do not "expand" as the "universe expands." The correct thing to say is that the space between all points in space increases.
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Could you explain your argument more thoroughly if you have the time? Lloyd had tried to explain a similar position, but I just can't figure out how it can be possible outside of a finite framework.
There are many ways of thinking of this. The number line example I give above is one way. Another would be to think of a uniform grid on an infinitely large sheet of paper. If this sheet of paper expands, then the distance between the vertices of a square on the grid paper will increase. But all the edges of the squares will increase in size; that is, there will not be any points that are closer after the expansion than they were before the expansion. This is what we really mean by "expansion of the universe"
~neutralino
If you haven't found something strange during the day, it hasn't been much of a day - John A. Wheeler.
I've been studying big-bang cosmology for about 20 years now, and those are some of the best examples yet. I stand corrected regarding "space between all points," but the argument still stands with respect to the direction of expansion for space. If space is expanding, or the points are being pushed away from each other, in the direction away from, say, point A, then the space between point A and every other point will be contracting towards the expanding space of every other point. If you're referring to the universe as everything, with no outside, then there is no need or place for space to expand - only particulate matter, which has its own debatable implications.
I like the sheet example, but it, like the balloon and raisin bread analogy, implies an expansion into non existence which is why the big bang seems illogical imo. The surrounding edges of space itself would have to expand into that which has no space, and the motion is unidirectional instead of omnidirectional.
Numerically, I guess it is easiest to understand, and in those terms, I think we have to consider that 1, 2 expanding as 2, 4, and then 4, 8, etc., also would have 8 expanding towards 4, and then 4 towards 2, etc..
That's implying that a finite universe must have boundaries, which is also not true.
An infinite universe can expand: it will of course still be infinite, but the distances between all points on the manifold will increase. This is, roughly, the definition of expansion.
Neutralino, infinity, or infinite universe is actually undefinable, as to size or expansion, within our logic, unless one uses a rational representation of infinity, such as; "Infinity equals finiteness times an n number of times finiteness, i.e., I=F^(n, c delimited potential). Just the same, IMO, I see no reason a true infinity would not possess an unlimited potential, but it's mere speculation... Still, again IMO, I think if one were to take a blank sheet universe, of primordial infinity, it would have all been a pure fluidic fundamental photonic substance, which actually produced the finiteness, we now know. I also think it would have had infinite mass potential, of infintesimal masses, of all these primordial photonic black holes, instantaneously exploding into the motion, we also now witness. Not that we witness the photons exploding into motion, but we witness the motion of some fundamental source. Why not the energy of something we fundamentally know exists, in our real universe, instead of ghost strings...? The maths of both micro-black-holes and macro black-holes, has already been somewhat worked out for years, and even string theory records it in AdS-CFT...
Regards,
Lloyd
"To develop the skill of correct thinking is in the first place to learn what you have to disregard. In order to go on, you have to know what to leave out; this is the essence of effective thinking." Kurt Godel "Time and space are modes in which we think and not conditions in which we live." Albert Einstein "The uncertainty principle is an absolute, finite, universal constant." L.G. "The tick-tick-tick of the cesium atom is a sliding-time-scaler constant of all finite universal motion." L.G.
I am also of the opinion that infiniteness cannot be equated with a finite number. As regards energy, apart from the energy that Llyod quoted, I have a feeling, Universe has some rest energy as well that we haven't been able to account for till date....
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Originally Posted by Lloyd Gillespie
Neutralino, infinity, or infinite universe is actually undefinable, as to size or expansion, within our logic, unless one uses a rational representation of infinity, such as; "Infinity equals finiteness times an n number of times finiteness, i.e., I=F^(n, c delimited potential). Just the same, IMO, I see no reason a true infinity would not possess an unlimited potential, but it's mere speculation... Still, again IMO, I think if one were to take a blank sheet universe, of primordial infinity, it would have all been a pure fluidic fundamental photonic substance, which actually produced the finiteness, we now know. I also think it would have had infinite mass potential, of infintesimal masses, of all these primordial photonic black holes, instantaneously exploding into the motion, we also now witness. Not that we witness the photons exploding into motion, but we witness the motion of some fundamental source. Why not the energy of something we fundamentally know exists, in our real universe, instead of ghost strings...? The maths of both micro-black-holes and macro black-holes, has already been somewhat worked out for years, and even string theory records it in AdS-CFT...
I dont think the Universe is infinite. Solely because it started off from apoint and a certain time has passed by thereby making the Universe finite and measureable. Even if it expands faster than light..
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Originally Posted by neutralino
Note that I never said that the universe "expands into" anything. The definition of "universe" is everything that exists; whether that be spacetime, or matter inside that spacetime. The universe may be infinite, or it may be finite; we don't really know yet. We do know, however, that the observable universe is much smaller than the total universe such that we can think of the universe as being infinite.
You're talking about "expansion of points" here, whereas I'm not. Points have no size, and so do not "expand" as the "universe expands." The correct thing to say is that the space between all points in space increases.
There are many ways of thinking of this. The number line example I give above is one way. Another would be to think of a uniform grid on an infinitely large sheet of paper. If this sheet of paper expands, then the distance between the vertices of a square on the grid paper will increase. But all the edges of the squares will increase in size; that is, there will not be any points that are closer after the expansion than they were before the expansion. This is what we really mean by "expansion of the universe"
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